I'm referring specifically to this sort of structure, where the notes cascade upwards or downwards but most often up and then back down. Many of the pieces I play (on piano) involve this rather heavily, and it's always a serious dilemma for me.

I have to sit down and carefully figure out the fingering, then play them very slowly over and over and over again until my hand can gloss through them in a fluid and clear motion, but this takes me literally 300-400 repetitions. Meanwhile I know many other players who can just sight read these things, not quickly on the first try, but it seems they just know the fingering by instinct and then they just go through it a few times and there you have it.

I don't know if this matters or not, but the stuff I have trouble with isn't as simple as seen in the example above...not just scales or something like that. I'm talking more about (for instance) Chopin's Op.10 No.12, which took me 9 months of slow repetition when I learned it a few years ago, and I'm no better now in that respect than I was then. It's infuriating.

If you know chords and scales well I guess identifying the chord(s) or scale(s), used in the arpeggio to learn, will help in order to identify what's going on in a broader perspective - not just what individual notes to play - thus easening the learning process even for the fingering. Other than that I think Babu is right about that you need to put in the practice.
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Ulf ÅkerstedtJul 26 '12 at 18:10

2 Answers
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Most classically trained pianists can gloss over arpeggios (and all their assorted variations) because their teachers made them do the repetitions you're describing beforehand. More generally, when you see pianists pick up complicated figures quickly, it's usually because they've seen them before, either in exercises or pieces they've already learned.

Along with chord inversions and scales, my piano teachers would have me practice arpeggios in every key. There's a sense behind the fingerings, and when that sinks in, it doesn't really matter what variation is thrown at you (for example, Chopin's revolutionary etude has a left hand part that is essentially a plain arpeggio with the second scale degree thrown in).

In the end, there's no substitute for putting the work in. To sight-read arpeggios faster, you need to practice playing them. You can continue as you've been doing, learning them piece by piece, but as you've noted, that approach is slow and can be frustrating.

Hanon's virtuoso pianist is useful in this situation; Around exercise 41 (page 66 of the full score I've linked) has fingerings for arpeggios in all 24 keys. I would use them as a light warmup whenever you practice, maybe 3 or 4 repetitions in whatever key you feel you need work in. Before too long, you won't find arpeggios to be much of an impediment at all.

To play arpeggios like this without all the figuring out you need to practise the common arpeggios by reading them off the page. What you are trying to get is an instant eye to hand recognition of common patterns. You can't achieve this by practising arpeggios from memory.